Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

THE INDEX THEOREM FOR QUASI-TORI

URN to cite this document: urn:nbn:de:bvb:703-opus4-11027

Title data

Chan, Tsz On Mario:
THE INDEX THEOREM FOR QUASI-TORI.
Bayreuth , 2013 . - 44 P.
( Doctoral thesis, 2012 , University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

[img] PDF
Thesis-MarioChan.pdf - Published Version
Available under License Creative Commons BY 3.0: Attribution .

Download (302kB)

Abstract

The Index theorem for holomorphic line bundles on complex tori asserts that some cohomology groups of a line bundle vanish according to the numbers of negative and positive eigenvalues of the associated hermitian form. In this thesis, this theorem is generalized to quasi-tori, i.e. connected complex abelian Lie groups which are not necessarily compact. In view of the Remmert–Morimoto decomposition of quasi-tori as well as the Künneth formula, it suffices to consider only Cousin-quasi-tori, i.e. quasi-tori which have no non-constant holomorphic functions. The Index theorem is generalized to holomorphic line bundles, both linearizable and non-linearizable, on Cousin-quasi-tori using L2-methods coupled with the Kazama–Dolbeault isomorphism and Bochner–Kodaira formulas.

Abstract in another language

Der Index-Satz für holomorphe Geradenbündel über komplexen Tori besagt, dass einige Kohomologiegruppen eines solchen Geradenbündels verschwinden, und zwar in Abhängigkeit von der Anzahl der negativen und positiven Eigenwerte der zugehörigen hermiteschen Form. In dieser Arbeit wird dieses Theorem auf Quasi-Tori, d.h. zusammenhängende komplexe abelschen Lie-Gruppen, die nicht unbedingt kompakt sind, verallgemeinert. In Anbetracht der Remmert–Morimoto Zerlegung von Quasi-Tori und der Künneth Formel genügt es Cousin-Quasi-Tori zu betrachten, d.h. Quasi-Tori ohne nicht-konstante holomorphe Funktionen. Es werden L2-Methoden zusammen mit dem Kazama–Dolbeault Isomorphismus und Bochner–Kodaira-Formeln verwendet, um den Index- Satz auf den Fall von holomorphen Geradenbündeln auf Cousin-Quasi- Tori zu verallgemeinern. Dabei sind linearisierbare und nicht-linearisierbare Geradenbündel zugelassen.

Further data

Item Type: Doctoral thesis (No information)
Additional notes (visible to public): msc: 14F17; msc: 32J25; msc: 32T27; msc: 46C05
Keywords: Algebraische Geometrie; Komplexe Differentialgeometrie; Funktionalanalysis; Quasi-tori; Toroidal groups; L2 estimates; Vanishing theorem
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-opus4-11027
Date Deposited: 24 Apr 2014 14:54
Last Modified: 24 Apr 2014 14:54
URI: https://epub.uni-bayreuth.de/id/eprint/157

Downloads

Downloads per month over past year